Question

Derive relation between relative magenetic permeability and magnetic susceptibility.

Answer 1

M=Xm.H 

Xm=M/H 

Xm=Mμ/B 

as H=B/μ 

and B=μo(H+M) 

Xm=(M.μ)/μo(H+M) 

so Xm=μr.M/(H+M)

substituting

M = χmH​ into B=μ0(H+M)​ 

Then factor the H.

 B=μo(H+M) and M=XmH 

B=μo(H+XmH) 

B=μoH(1+Xm) 

so μH=μoH(1+Xm) 

μ/μo=μr 

Xm=1-μr

Answer 2

Answer:

The relation between relative permeability and magnetic susceptibility is given by μ r = 1 + χ ̲ .

Explanation:

• The intensity or degree of magnetization (I) of a material in response to the intensity of the magnetising force (H) of an applied magnetic field is indicated by magnetic susceptibility (m) (B).
• Magnetic permeability is a material attribute that describes the amount of magnetising force (H) that a material experiences when a magnetic field is applied (B).

Now,

χm=I/H

and, μ=B/H

also, μr=μ/μ0 (relative permeability)

Magnetization due to applied field (B0) and magnetization due to induced magnetism will combine to form the net field (Bi),

B=B0+Bi

Where, B0=μ0H and Bi=μ0I

⇒B=μ0(H+I)

⇒BH=μ0(1+I/H)

Substituting μ=B/H and χm=I/H in the above equation, we get:

μ=μ0(1+χm)⇒μ/μ0=(1+χm)⇒μr=(1+χm)

Hence proved.

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